Gas Laws

Pressure-Volume State

pressure times volume

A gas state can be described by pressure, volume, and absolute temperature. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Read pressure and volume

This gas state has pressure 2 pascals and volume 6 cubic meters.

p=2 PaV=6 m3p = 2\ \text{Pa}\qquad V = 6\ \text{m}^{3}
Gas stateThe piston width is computed from the volume.6 m^32 Pa 300 Kstate

Multiply pressure by volume

Pressure times volume has units of energy in this unit system.

pV=2 Pa⋅6 m3pV = 2\ \text{Pa}\cdot 6\ \text{m}^{3}

Compute the product

Multiplying 2 by 6 gives 12 joules.

pV=12 JpV = 12\ \text{J}
Gas stateThe piston width is computed from the volume.6 m^32 Pa 300 Kstate

Pressure scales the product directly

Hold volume at 6 cubic meters. The diagram shows the middle row; more pressure makes a larger pressure-volume product.

pVpV1 Pa6 m36 J2 Pa6 m312 J3 Pa6 m318 J\begin{array}{c|c|c}p&V&pV\\1\ \text{Pa}&6\ \text{m}^{3}&6\ \text{J}\\2\ \text{Pa}&6\ \text{m}^{3}&12\ \text{J}\\3\ \text{Pa}&6\ \text{m}^{3}&18\ \text{J}\\\end{array}
Gas stateThe middle table row is the checked diagram.6 m^32 Pa 300 Kstate

Volume also scales the product directly

Now hold pressure at 2 pascals. Larger volume gives a larger pressure-volume product.

pVpV2 Pa3 m36 J2 Pa6 m312 J2 Pa9 m318 J\begin{array}{c|c|c}p&V&pV\\2\ \text{Pa}&3\ \text{m}^{3}&6\ \text{J}\\2\ \text{Pa}&6\ \text{m}^{3}&12\ \text{J}\\2\ \text{Pa}&9\ \text{m}^{3}&18\ \text{J}\\\end{array}
Gas stateThe middle table row is the checked diagram.6 m^32 Pa 300 Kstate